Questions: If we reject the null hypothesis, we say: there is not sufficient evidence to support the alternative hypothesis

Transcript text: If we reject the null hypothesis, we say: there is not sufficient evidence to support the alternative hypothesis

Solution

Solution Steps

Step 1: Understanding the Hypothesis Testing Framework

In hypothesis testing, we start with two competing hypotheses: the null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)). The null hypothesis typically represents a statement of no effect or no difference, while the alternative hypothesis represents a statement that indicates the presence of an effect or difference.

Step 2: Analyzing the Statement

The statement in question is: "If we reject the null hypothesis, we say: there is not sufficient evidence to support the alternative hypothesis."

In hypothesis testing, rejecting the null hypothesis (\(H_0\)) implies that we have found sufficient evidence to support the alternative hypothesis (\(H_1\)). Therefore, the statement is logically incorrect.

Step 3: Conclusion

Since rejecting \(H_0\) indicates sufficient evidence for \(H_1\), the statement is false.